Question

A 930 kg sports car collides into the rear end of a 2300 kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 3.1 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact.

What was that speed?

Answer 1

Momentum before impact = momentum after impact of both vehicles:

930*v1 + 0 = (930+2300)*v2,

where v1 = speed of sports car before impact and v2 = speed of both vehicles after impact.

From above, v1 = 3230*v2/930 ...........1)

Frictional force acting in horizontal position after impact of both vehicles = 3230*g*0.80 ..............2)

Total kinetic energy of both cars after impact

= 1/2*m*v*v= 1/2*3230*v2*v2 .............3)

From 2) & 3) above

1/2*3230*v2*v2 = 3230*g*.80*3.1, from where we get

v2 = 6.97 m/s

From 1) above, we get

v1 = 3220*6.63/920 = 24.21 m/s